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Some say yes and some no (note I am ignoring here the issue of cointegration). Say there is no cointegration.

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    $\begingroup$ Maybe, some say yes and some say no because they, unlike your question, refer to a specific purpose - estimation, inference, forecasting etc. The answer may depend on the purpose. A nonstationary VAR in levels may for example forecast well, but not allow to use standard inferential tools (e.g., conduct t-tests with standard normal critical values). $\endgroup$ Commented Mar 27, 2019 at 7:43
  • $\begingroup$ Chris Brooks in Introductory Econometrics for Finance, "If one wishes to use hypothesis tests, either singly or jointly, to examine the statistical significance of the coefficients, then it is essential that all of the components in the VAR are stationary." "However, many proponents of the VAR approach recommend that differencing to induce stationarity should not be done. They would argue that the purpose of VAR estimation is purely to examine the relationships between the variables, and that differencing will throw information on any long-run relationships between the series away." $\endgroup$
    – user54285
    Commented Mar 27, 2019 at 18:14

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